The Einstein field equations of General Relativity are a system of non-linear partial differential equations for the space-time metric. Remarkably, exact solutions to these non-linear equations can be obtained by reformulating the problem as a Riemann-Hilbert  boundary value problem of a particular type and solving a matricial Wiener-Hopf factorization problem.In this talk we generalise the Riemann-Hilbert approach and introduce an invariance problem providing other types of factorisation that also yield solutions to the field equations, as well as a new solution generating method by matrix multiplication.Based on joint work with Gabriel L. Cardoso.